Rotate 3d vector value into a single axis using a rotation quaternion

Question

I want to rotate the whole value of a 3d vector into one axis using quaternion rotations.

The reason behind is that I want to align the X and Y Axis of my smartphone with the X and Y Axis of my vehicle in order to detect lateral and longitudinal acceleration separated on these two axis. Therefore I want to detect the first straight acceleration of the car and rotate the whole acceleration value into the heading axis (X-Axis) of the phone assuming a straight forward motion.

How do I achieve this?

Answer 1

I got it myself while this Link helped me a lot.

In the end I just needed to define the destination axis as a Vector V(Magnitude_Source, 0, 0), calculate the angle between V and the source vector and rotate the source vector.